A personal view on statistics in earth sciences

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It is 2019 and it is spring time in Vienna again. The night train from Hamburg to Vienna was as always a great experience and so the conference was set up for a good start. The sun is giving everybody a big smile (at least for the start) and so and eventful week lies ahead of us.

The first day was fully covered for me by sea level science. The sea level session covered as always a wide range of topics. From reconstructions over land movements, from GIA to the political site of the problem. Unfortunately, my favorite topic, the palaeo-reconstructions were only covered by a very small number of talks (probably just one).

I have also to get used to the new schedule of seven talks per session, but I will certainly write about it more later this week. I also went to a poster session, which are now in parallel to the talk-sessions. So a lot of changes, which all need some adaptions.

During the week I will have a talk and a poster, but both will happen towards the end. I am looking forward for many interesting topics, talks and posters and of course the most important part of a conference: meeting other scientists.

Many talks surrounded the available data and their interpretation. In this context it is a very complex task to bring together on the one side the many different proxies and evidences of sea-level height during that period and on the other side to explain their causes by the changes of ice-sheets in the higher latitudes and the reaction on them by the Earth. As a consequence there were many interesting discussions surrounding this field and many different viewpoints were heard. Specific questions around when the last interglacial exactly started, how high the sea-level was during that period and how the exact evolution of sea-level happened during that time were often discussed during this week. Most discussions were evidence driven, trying to make sense of the sometimes contradicting results and their uncertainties.

Also the understanding of the consequences of these results played an important role, as sea-level change is not happening isolated. It requires the build up or melting of ice shoot and with it a change in climate. In a climate system, as we know from looking around us today, that is highly connected all the climate sub-components, especially atmosphere, cryosphere and ocean have to tell the same story.

Myself have presented a poster on the last interglacial sea-level evolution and had several interesting discussions on this topic. Also the field trip, which showed us the study fields of salt marches, which are used to investigate Holocene sea-level change at the East American coast was very informative. Seeing the data collection first hand always helps to understand the topic better and getting better results at the computer in your own office. All in all it was a great opportunity for me, which was made possible by the financial contribution by the organisers, which allowed me to attend.

It was the fourth day and at this time a conference gets a bit exhausting. I started the day with a visit to statistical post-processing and walked then on to the sea level session for the rest of the morning. As I have worked in my past position in sea-level science the topic is still very familiar for me. Especially the large range of topics, from palaeo-reconstructions to engineering advice makes a visit to such a session always an interesting adventure. After lunch I switched to the precipitation databases session, which was after the break followed with homogenisation approaches. The end of the day was as always filled with the poster session.

Tomorrow, I will finally have the opportunity to show my own work. In the afternoon I will have my talk on seasonal prediction and in the evening a poster on past sea-level change. Traditionally, the friday tends to be quite empty and it is usually not so good to have the contributions so late in a conference, but I am sure it will still be an interesting final day.

The new year has started and in the recent weeks two new papers with myself in the author list have been published. Both are covering a wide spectrum and my contribution was in both cases more something I would classify as statistical assistance. Therfore, I will keep my comments brief at this place and just quickly introduce the topics.

This paper is about the sea-level height at Bermuda at roughy 70,000 years back. It is mainly a geological paper and focusses on the evidence from speleotherms, that indicate that sea-level was positive compared to today at that time. That is important, because the rest of the world has in many places lower than modern sea-level at that time. A plot in the later part of the paper shows, that the difference at different locations in the carribean can be up to 30-40m. Explained can this be with GIA modelling and the paper is therefore a good help to better calibrate those models.

The second paper focusses on the hindcast skill of two decadal forecasting systems of the Atlantic meridional overturning circulation (AMOC). It shows that both system have significant hindcast skill in predicting the AMOC for up to five years in advance, while an uninitialised model run has not. The time series for evaluationg the systems are still quite short, but the extensive statistics in the paper allows to transparently follow the argument, why the system do have this capability.

In my final post on the background on the recently published paper, I would like to take a look into the future of this kind of research. Basically it highlights again what I have already written at different occasions, but putting it together in one post might make it more clear.

The datasets and their basic interpretation are the most dramatic point, where I expect the greatest steps forward in the next years. Some paper came out recently that highlight some problems, like the interpretation of coral datasets. We have to make steps forward to understand the combination of mixed datasets and this can only happen when future databases advance. This will be an interdisciplinary effort and so challenging for all involved.

The next field involved are the models. The analysis is currently done with simple models, which has its advantages and disadvantages. New developments are not expected immediately and so more the organisation of the development and sharing the results of the models will be a major issue in the imminent future. Also new ideas about the ice sheets and their simple modelling will be needed for similar approaches as we had used in this paper. Statistical modelling is fine up to a point, but there are shortcomings when it goes to the details.

The final field is the statistics. Handling sparse data with multidimensional, probably non-gaussian uncertainties has been shown as complicate. There needs to be new developments of statistical methodology, which are simple on the one side, so that every involved discipline can understand them, but also powerful enough to solve the problem. We tried in our paper the best to develop and use a new methodology to achieve that, but there are certainly different approaches possible. So creativity is needed to generate methodologies, which do not only deliver a value for the different interesting parameters, but also good and honest uncertainty estimates.

Only when these three fields develop further we can really expect to get forward with our insights into the sea-level of the last interglacial. It is not a development, which will happen quickly, but I am sure that the possible results are worth the efforts.

After the new paper is out it is a good time to think about the current status on the main question it covered, the sea-level during the LIG. Usually I do not want to generalise too much in this field, as there is currently a lot going on, many papers are in preparation or have just been published and the paper we have just published was originally handed in one and a half years ago. Nevertheless, some comments on the current status might be of interest.

So the main question the most papers on this topic cover is: How high was the global mean sea-level during the last interglacial. There were some estimates in the past, but when you ask most people who work with this topic they will answer more than six metre higher than today. That is of course an estimate with some uncertainty attached to it and currently most expect that it will not have been much higher than about nine metres than today. There are several reasons for this estimate, but at least we can say that we are quite sure that it was at least higher than present. From my understanding, geologists are quite certain that at least for some regions this is true and even when the data is sparse, meaning the number of data points low, it is very likely that this was also the case for the global mean. Whether it is 5, 6 or 10 metre higher is a more complicate question. It will still need more evaluation until we can make more certain statements.

Another question on this topic are the start point, end point and duration of the high stand. This question is very complex, as it depends on definitions and the problem that in many places only the highest point of sea-level over the duration of the LIG can be measured. That makes it very complex to say something definitive especially on the starting point. As such, our paper did not really made a statement on this, as it just shows that data from boreholes and from corals are currently not stating the same answer.

The last question everybody asks is the variability of the sea-level during the LIG. Was it just one big up and down or were there several phases with a glaciation phase in the middle. Or where there even more phases than two? Hard questions. The most reliable statements say that there are at least two phases, while from my perspective our paper shows that it is currently hard to make any statement basing on the data we used. But also here, new data might give us the chance to make better statements.

So there are still many questions to answer in this field and I hope the future, on which I will write in my last post on this topic, will bring many more insights into this field.

Within the new paper we developed and modified a data assimilation scheme basing on simple models and up to a point Bayesian Statistics. In the last post I talked about the advantages and purposes of simple models and this time I would like to talk about their application.

As already talked about, we had a simple GIA model available, which was driven by a statistical ice sheet history creation process. From the literature, we had the guideline that the sea level over the past followed roughly the dO18 curve, but that high deviations from this in variation and values can be expected. As always in statistics there are several ways to perform a task, basing on different assumptions. To design a contrast to the existing literature, the focus was set to work with an ensemble based approach. Our main advantage here is that we get at the end individual realisations of the model run and can show individually how they perform compared to the observations.

The first step in this design process of the experiment is the question how to compare a model run to the observations. As there were several restrictions from the observational side (limited observations, large two-dimensional uncertainties etc.), we decided to combine Bayesian statistics with a sampling algorithm. The potential large number of outliers also required us to modify the classical Bayesian approach. As a consequence, we were able at that point to estimate for each realisation of a model run a probability.

In the following the experimental design was about a general strategy, how to create the different ensemble members so that they are not completely random. Even with the capability to be able to create a lot of runs, even realisations in the order of 10,000 runs are not sufficient to determine a result without a general strategy. This lead us to a modified form of a Sequential Importance Resampling Filter (SIRF). The SIRF uses a round base approach. In each round a number of model realisations are calculated (in our case 100) and afterwards evaluated. A predefined number of them (we used 10), the best performers of the round, are taken forward to the next and act as seeds for the new runs. As we wanted a time-wise determination of the sea-level, we chose the rounds in this dimension. Every couple of years (in important time phases like the LIG more often) a new round was started. In each the new ensembles branched from their seeds with anomaly time series for their future developments. Our setup required that we always calculate and evaluate full model runs. To prevent that very late observations drive our whole analysis, we restricted the number of observations taken into account for each round. All these procedures led to a system, where in every round, and with this at every time step of our analysis, the ensemble had the opportunity to choose new paths for the global ice sheets, deviating from the original dO18 curve.

As you can see above, there were many steps involved, which made the scheme quite complicate. It also demonstrate that standard statistics get to its limits here. Many assumptions are required, some simple and some tough ones, to generate a result. We tried to make these assumptions and our process as transparent as possible. As such, our individual realisations, basing on different model parameters and assumptions on the dO18 curve, show that it is hard to constrain the sea-level with the underlying datasets for the LIG. Of course we get a best ice-sheet history under our conditions, that is how our scheme is designed, but it is always important to evaluate whether the results we get out of our statistical analysis make sense (basically if assumptions hold). In our case we could say that there is a problem. It is hard to say whether it is the model, the observations or the statistics itself which make the largest bit of it, but the observations are the prime candidate. Reasons are shown in the paper together with much more information and discussions on the procedure and assumptions.